Solve  \[\frac{3x^2+2x+1}{x-1}=3x+1\]for $x$.
Cross-multiplication gives  \[3x^2+2x+1=(x-1)(3x+1)=3x^2-2x-1.\]Therefore \[4x=-2\]and $x=\boxed{-\frac{1}2}$.